Question: Simplify the following expression: $z = \dfrac{7a^2 - 56a - 63}{a - 9} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $7$ , so we can rewrite the expression: $ z =\dfrac{7(a^2 - 8a - 9)}{a - 9} $ Then we factor the remaining polynomial: $a^2 {-8}a {-9} $ ${-9} + {1} = {-8}$ ${-9} \times {1} = {-9}$ $ (a {-9}) (a + {1}) $ This gives us a factored expression: $\dfrac{7(a {-9}) (a + {1})}{a - 9}$ We can divide the numerator and denominator by $(a + 9)$ on condition that $a \neq 9$ Therefore $z = 7(a + 1); a \neq 9$